1. Technical Field
The present disclosure relates to the field of global navigation satellite systems, including techniques for computing cinematic parameters, such as the position, velocity, acceleration, trajectory, etc., of the receiving apparatus operating in the global navigation satellite systems.
2. Description of the Related Art
A GNSS (Global Navigation Satellite System) receiver, for example a GPS (Global Positioning System), receives properly formatted electromagnetic signals transmitted by a constellation of satellites orbiting the earth. These signals contain information which can be used to compute receiver/user position, velocity and time, such as space vehicle ECEF (Earth Centered Earth Fixed) position, GPS time, transmitter clock error, ionospheric delay.
A so called tracker module of the GNSS receiver performs measurements about satellites in view. Two quantities of interest are detected: the difference between transmission and arrival times, i.e. the distance between receiver/user and the satellite (pseudorange) and the Doppler shift from nominal carrier frequency; the latter quantity is referred as “frequency”.
To estimate the receiver (user's) position, velocity and time (PVT) two main approaches are employed according to known GPS techniques. One is the Least Square approach according to which the solution is reached using an estimating algorithm without dependence on past solution data. This algorithm is iterative, i.e. the solution is obtained executing the algorithm multiple times using the same actual tracker data. At every iteration a better solution is generally obtained, until the best estimate (the one minimizing the square of the error) is yielded. Position and velocity computations are loosely coupled, i.e. position derives by pseudoranges, while velocity is function of frequencies.
The other standard solution is to employ a Kalman Filter (KF). This is a recursive algorithm, in sense that solution at step t depends on the one obtained at t-1. Moreover PVT computation is tighter for Kalman Filter approach than for the Least Square method, i.e. position computation may be made dependent on a whole set of current measurements (pseudorange and dopplers) and from previous position and velocity.
In common practice, the Kalman Filter generally provides the optimal performance when the signal is affected by White Gaussian Noise, outperforming the Least Square algorithm. As an example, it has been shown that during 95% of the time, the Least Square estimation error is less than 15 m while the Kalman Filter estimation error is less than 4 m. This example refers to data acquired in a 6 hour long frame while receiver stood in optimal condition (i.e. static, full sky visibility, no reflections).
GNSS receivers are known that implement both algorithms: Least Square is used to deliver the first fix at the start-up of the receiver, after a long signal outage, while steady state working conditions see the Kalman Filter being chosen.
U.S. Patent Application No. 2010/0026568 describes a method for selecting the Least Square algorithm or the Kalman Filter algorithm in order to manage situations in which the GPS receiver has gone through a tunnel and is coming out of the same.